Input-dependent Suppression of Chaos in Recurrent Neural Networks

Neuronal responses arise from an interaction between spontaneous activity and responses driven by external inputs. Experiments studying cortical circuits reveal a striking similarity between the magnitude and complexity of intrinsic and input-generated activity. How does a network generating complex activity remain sensitive to external inputs? This seems unlikely for a network in which input-driven responses add linearly to ongoing activity generated by stochastic noise generators. We developed a mean-field theory and used recurrent network models to distinguish between this type of external noise and chaotic background generated by strong coupling within the circuit. As a result of a highly nonlinear relationship between input- and internally generated activity, we show that intrinsic \textbf{\textit{noise}} is sensitive to the amplitude and the spatiotemporal structure of the input. We find that input not only drives responses, it also actively suppresses spontaneous activity, leading to a phase transition in which the chaotic background is absent. Although the power spectrum of the spontaneous activity falls exponentially from zero, the phase transition reveals a \textbf{\textit{resonant}} frequency at which relatively a weak input suppresses chaos. As long as the input drives the system across the phase transition, a spontaneously active network can work with coupling strong enough to allow large signal amplification and selectivity without the complex background interfering with sensory processing.